Here is the full list of all 10 Keep Talking and Nobody Explodes trophies - there are 4 bronze, 5 silver and 1 gold.
Defuse all bombs in the "Exotic" section.
Defuse all bombs in the "Extreme" section.
Defuse 100 bombs.
Defuse all bombs in the "Challenging" section.
Defuse all bombs in the "Needy" section.
Defuse all bombs in the "Moderate" section.
Disarm 100 modules.
Disarm each type of module at least once.
Defuse all bombs in "The Basics" section.
Defuse "The First Bomb".